New Twiddle

components.my-component.js

import Ember from 'ember';
import _ from "lodash";

const { computed, get, set } = Ember;

export default Ember.Component.extend({
  items: [],
  allItems: computed.alias('items'),
  selectedItems: [],
 
  allItemsSelected: computed('allItems.length', 'selectedItems.length', function(){
    return get(this, 'allItems').length === get(this, 'selectedItems').length;
  }),
  
   someItemsSelected: computed('allItems.length', 'selectedItems.length', function(){
    return get(this, 'selectedItems').length > 0;
  }),
    
  actions: {
    toggleAllItems: function(){
      let allSelected;

      if (get(this, 'someItemsSelected')){
       set(this, 'selectedItems', []);
        allSelected = false;
      } else {
       set(this, 'selectedItems', get(this, 'allItems'));
        allSelected = true;
      }
      
      let $el = this.$('.checkbox');
      if (allSelected) {
        $el.prop('checked', true);
      } else {
        $el.prop('checked', false);
      }
    },
    selectItem: function(item){
      let selectedItems = get(this, 'selectedItems').toArray();
      
      if (selectedItems.includes(item)) {

        set(this, 'selectedItems', _.without(selectedItems, item));
      } else {
        set(this, 'selectedItems', _.union(selectedItems, [item]));
     	}
    }
  },
});

controllers.application.js

import Ember from 'ember';

export default Ember.Controller.extend({
  appName: 'Ember Twiddle',
  
  items: [ {name: 'milk'}, {name: 'eggs'}, {name: 'cheese'} ]
});

templates.application.hbs

<h1>My Grocery List</h1>
<br>
{{my-component items=items}}
<br>
<br>

To recreate this bug:
<ul>
	<li> Select one or more items </li>
  <li> Uncheck them - note that the total count and checkbox reset correctly to 0</li>
  <li> Select one or more items (not all three) and note 'allItemsSelected' is false </li>
  <li> Check the indeterminate checkbox to unselect all items</li>
  <li> Note that even though 'allItemsSelected' is false, the checkbox is selected</li>
</ul>

templates.components.my-component.hbs

{{input
	class="checkbox"
	type="checkbox"
  checked=allItemsSelected
  indeterminate=(xor allItemsSelected someItemsSelected)
  change=(action "toggleAllItems")}}

{{selectedItems.length}} of {{allItems.length}}
( allItemsSelected == {{allItemsSelected}})
<br>

{{#each items as |item|}}
	<div>
	<input
  	type="checkbox"
    checked={{contains item selectedItems}} 
    onchange={{action "selectItem" item}}>
  {{item.name}}
  </div>
  <br>
{{/each}}

twiddle.json

{
  "version": "0.12.1",
  "EmberENV": {
    "FEATURES": {}
  },
  "options": {
    "use_pods": false,
    "enable-testing": false
  },
  "dependencies": {
    "jquery": "https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.3/jquery.js",
    "ember": "2.12.0",
    "ember-template-compiler": "2.12.0",
    "ember-testing": "2.12.0"
  },
  "addons": {
    "ember-data": "2.12.1",
    "ember-composable-helpers": "1.1.3",
    "ember-lodash": "4.17.4",
    "ember-truth-helpers": "1.3.0"
  }
}